The photonic spin Hall effect in transmission is a transverse beam shift of the out-coming beam depending on polarization of the incoming beam. The effect can be significantly enhanced by materials with high anisotropy. We report, to the best of our knowledge, the first experimental demonstration of the photonic spin Hall effect in a multilayer hyperbolic metamaterial at visible wavelengths (wavelengths of 520 and 633 nm). The metamaterial is composed of alternating layers of gold and alumina with deeply subwavelength thicknesses, exhibiting extremely large anisotropy. The angle-resolved polarimetric measurements showed the shift of 165 μm for the metamaterial of 176 nm in thickness. Additionally, the transverse beam shift is extremely sensitive to the variations of the incident angle changing theoretically by 270 μm with 1 milli-radian (0.057°). These features can lead to minituarized spin Hall switches and filters with high angular resolution.